31 ideas
| 1606 | You have to be a Platonist to debate about reality, so every philosopher is a Platonist [Roochnik] |
| 1595 | Philosophy aims to satisfy the chief human desire - the articulation of beauty itself [Roochnik] |
| 1571 | 'Logos' ranges from thought/reasoning, to words, to rational structures outside thought [Roochnik] |
| 1572 | In the seventeenth century the only acceptable form of logos was technical knowledge [Roochnik] |
| 1573 | The hallmark of a person with logos is that they give reasons why one opinion is superior to another [Roochnik] |
| 1592 | Logos cannot refute the relativist, and so must admit that it too is a matter of desire (for truth and agreement) [Roochnik] |
| 1593 | Human desire has an ordered structure, with logos at the pinnacle [Roochnik] |
| 1603 | Logos is not unconditionally good, but good if there is another person willing to engage with it [Roochnik] |
| 1598 | We prefer reason or poetry according to whether basics are intelligible or not [Roochnik] |
| 1584 | Modern science, by aiming for clarity about the external world, has abandoned rationality in the human world [Roochnik] |
| 1591 | Unfortunately for reason, argument can't be used to establish the value of argument [Roochnik] |
| 1599 | Attempts to suspend all presuppositions are hopeless, because a common ground must be agreed for the process [Roochnik] |
| 13838 | A decent modern definition should always imply a semantics [Hacking] |
| 13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
| 13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
| 13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
| 13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
| 13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
| 13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
| 13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
| 13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
| 13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
| 13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
| 7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
| 10059 | In mathematic we are ignorant of both subject-matter and truth [Russell] |
| 7556 | A collection is infinite if you can remove some terms without diminishing its number [Russell] |
| 1605 | Reality can be viewed neutrally, or as an object of desire [Roochnik] |
| 7554 | Self-evidence is often a mere will-o'-the-wisp [Russell] |
| 1577 | Relativism is a disease which destroys the possibility of rational debate [Roochnik] |
| 1578 | If relativism is the correct account of human values, then rhetoric is more important than reasoning [Roochnik] |
| 1596 | Reasoning aims not at the understanding of objects, but at the desire to give beautiful speeches [Roochnik] |